Reprinted  from  The  Astrophysical  Journal,  Vol.  XXXIII,  No.  i,  January  1911 


«■  \ P \ 


PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


By  . 

GORDON  SCOTT  FULCHER 


A DISSERTATION  SUBMITTED  TO  THE  FACULTY  OF  CLARK  UNIVERSITY,  WORCES- 
TER, MASS.,  IN  PARTIAL  FULFILMENT  OF  THE  REQUIREMENTS  FOR  THE 
DEGREE  OF  DOCTOR  OF  PHILOSOPHY,  AND  ACCEPTED  ON  THE  RECOMMEN- 
DATION OF  PROFESSOR  A.  G.  WEBSTER,  JUNE  14,  1910 


Revised  December  28,  1910 


PRINTED  AT  THE  UNIVERSITY  OF  CHICAGO  PRESS 


§35 

T^s® 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 

By  GORDON  SCOTT  FULCHER 

The  two  phenomena  of  greatest  significance  in  connection  with 
canal  rays  are  well  known  to  be  the  simultaneous  electrostatic 
and  magnetic  deflection  of  the  rays,  first  obtained  by  W.  Wien, 
and  the  Doppler  effect,  which  J.  Stark  discovered  to  be  shown  by 
light  from  the  path  of  the  canal  rays.  The  Wien  experiment 

enables  us  to  determine  the  velocity  and  mean  value  of  — of  the 

m 

constituent  rays;  the  Stark  effect  gives  us  directly  the  speed  in 
the  line  of  sight  of  the  sources  of  the  light  showing  the  effect. 
Two  years  ago,  from  a summary  and  comparison  of  the  experi- 
mental results  reported  by  W.  Wien,  J.  J.  Thomson,  J.  Stark, 
F.  Paschen,  and  others,1  it  seemed  evident  that  the  distribution  of 
velocities  among  the  canal  rays  is  quite  different  from  that  among 
the  sources  of  the  light  showing  the  Stark  effect.  It  appeared  to 
be  necessary  to  conclude  that  the  canal  rays  cannot  themselves 
be  the  chief  sources  of  the  light  in  question,  as  has  been  generally 
assumed.2 

THE  HYPOTHESIS 

An  alternative  hypothesis  was  suggested.  The  only  other 
molecules  present  with  velocities  great  enough  for  them  to  be  the 
sources  sought  are  those  gas  molecules  which  have  been  hit  by 
the  canal  rays  and  thus  have  acquired  a velocity  great  or  small 
according  to  the  squareness  of  the  collision.  If  we  suppose  this 
molecular  phenomenon  to  obey  the  laws  of  ordinary  impact  between 
solid  bodies,  the  momentum  given  the  gas  molecule  will  vary  up 
to  a maximum  value  of  the  same  order  as  that  of  the  bombarding 
ray,  depending  on  the  relative  masses  of  the  two  molecules  and 
on  the  coefficient  of  restitution.  Will  the  Doppler  effect  to  be 
expected  if  these  hit  molecules  emit  light  agree  in  all  essential 

1 G.  S.  Fulcher,  “Our  Present  Knowledge  of  Canal  Rays,”  Smithsonian  Misc. 
Collections , 52,  295-324,  1909. 

2 Ibid.,  p.  322. 


28 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


29 


details  with  the  Stark  effect  as  observed  ? A statistical  computa- 
tion, explained  in  detail  below  (p.  41),  showed  that  a satisfactory 
agreement  was  obtained  if  the  following  assumptions  were  made: 

1.  That  the  intensity  of  the  light  emitted  as  a result  of  each 
impact  is  proportional  to  the  energy  transmitted  to  the  hit  mole- 
cule, but 

2.  That  the  hit  molecule  emits  no  light  unless  the  energy  so 
transmitted  exceeds  a certain  minimum  supposed  to  be  equal  to 
that  necessary  to  produce  ionization;  and 

3.  That  the  hitting  molecules  emit  no  light  of  the  kind  show- 
ing the  Stark  effect  as  a result  of  the  collision.  Of  these,  the  first 
has  since  been  experimentally  verified  (see  below),  the  second  is 
rendered  probable  by  other  experimental  evidence,  and  the  third, 
rather  more  difficult  to  accept,  will  be  shown  later  to  be  a necessary 
assumption  which  perhaps  can  be  made  more  plausible  by  the 
consideration  that  most  of  the  hitting  charged  rays  may  be  neu- 
tralized by  the  collisions  which  ionize  the  hit  molecules.  Hence 
if  the  hitting  molecules  thus  neutralized  emit  any  light,  it  is  not 
the  series-line  spectrum  which  is  emitted  by  the  ionized  molecules 
and  which  alone  shows  the  Stark  effect. 

It  is  possible  then  to  reconcile  the  results  of  the  deflection 
experiments  with  the  Stark  effect  if  we  assume  that  the  sources 
of  the  light  showing  this  effect  are  the  gas  molecules  hit  and  ion- 
ized by  the  canal  rays  rather  than  the  canal  rays  themselves.1 

EXPERIMENTAL  EVIDENCE 

If  this  hypothesis  is  correct  the  intensity  of  the  light  from  a 
canal-ray  beam  should  vary  directly  as  the  number  of  collisions 
per  unit  time,  per  unit  length  of  path,  that  is,  with  the  pressure 
of  the  gas,  providing  the  number  and  velocity  of  the  canal  rays 
are  kept  constant. 

The  following  apparatus,  shown  diagrammatically  in  Fig.  1, 
has  been  designed  to  test  this  deduction.  It  is  so  arranged 
that  the  pressure  of  the  gas  in  the  canal-ray  chamber  back  of  the 
cathode  can  be  varied  in  the  ratio  of  one  to  twenty  without  chan- 
ging the  pressure  in  the  discharge  chamber,  which  determines  the 

1 Ibid. 


35847 


30 


GORDON  SCOTT  FULCHER 


cathode-fall  of  potential,  that  is,  the  number  and  velocity  of  the 
canal  rays.  In  one  experiment  hydrogen  gas  from  the  reservoir 
where  the  pressure  is  maintained  at  a certain  constant  value  of 
about  5 cm  of  mercury,  passes  slowly  and  continuously  through 


a capillary  tube  (io  cm  long  and  with  a bore  about  0.009  cm  in 
diameter)  and  some  purifying  tubes  to  the  discharge  chamber. 
The  pressure  here  is  about  0.1  mm  of  mercury.  From  this 
chamber  a single  hole  in  the  aluminum  cathode  (0.05  cm  in 
diameter  and  1 cm  long)  leads  to  the  canal  chamber,  which  is 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


3i 


maintained  at  a pressure  of  about  .005  mm  of  mercury  by  a 
Gaede  mercury  pump  to  which  it  is  connected  by  large  tubes. 
The  hole  in  the  cathode  thus  behaves  like  a porous  plug  of  a single 
pore.  After  equilibrium  is  established,  these  pressure  relations 
can  be  maintained  indefinitely,  and  the  intensity  of  the  light 
emitted  when  the  canal  rays  pass  through  gas  at  the  low  pressure 
maintained  in  the  canal  chamber  can  be  measured  at  leisure.1 

On  the  other  hand  the  pump  may  be  stopped  and  the  pressure 
allowed  to  become  the  same  on  both  sides  of  the  cathode  and  equal 
to  the  pressure  formerly  existing  only  on  the  discharge-chamber 


c 

a 

b 


Fig.  2. — Photographs  of  the  canal-ray  beam 

a , Beam  through  gas  at  low  pressure  (0.005  mm) 

b,  Beam  through  gas  at  higher  pressure  (o.  1 mm) 

c , Extra-focal  image  of  beam,  higher  pressure 

side.  Conditions  in  the  discharge  chamber  will  now  be  the  same 
as  in  the  first  experiment;  hence  the  current  and  the  cathode-fall 
of  potential,  and  therefore  the  number  and  velocity  of  the  canal 
rays,  will  be  the  same  in  both  cases,  though  the  pressure  in  the  canal 
chamber  is  quite  different.  Hence  the  intensity  of  the  light  from 
the  canal-ray  beam  should  vary  in  the  same  ratio  as  the  pressure 
of  the  gas  in  the  canal  chamber,  if  our  hypothesis  is  correct. 

To  measure  the  intensity  of  the  light,  the  beam  was  photo- 
graphed with  an  ordinary  camera.  The  time  of  exposure  was 
adjusted  so  that  in  all  cases  images  of  about  the  same  density  were 
obtained.  The  camera  was  thrown  slightly  out  of  focus  so  as  to 
secure  broader  images  whose  density  could  be  more  easily  compared 

1 To  avoid  confusion,  the  discussion  of  certain  details  of  the  apparatus  is  post- 
poned to  the  end  of  the  paper. 


32 


GORDON  SCOTT  FULCHER 


by  the  use  of  a spectrophotometer  (see  Fig.  2).  The  intensity  of 
the  light  was  assumed  proportional  to  the  density  of  the  image 
divided  by  the  time  of  exposure.  The  pressure  was  measured 
with  a McLeod  gauge  connected  to  the  canal  chamber.  The 
results  for  two  cathode-falls  of  potential  are  given  in  the  following 
table. 

TABLE  I 


Cathode- 

Fall 

Volts 

Pressure 

mm  of  Eg 

Time  of 
Exposure 

t 

Density  of 
Image 

D 

Intensity  of 
Light  I=j 

A 

U 

D 

P* 

/. 

P* 

P . 

3900 

i 1 
! 2 

O.  102 
O.OO53 

60  sec. 
1200  “ 

O.41 

O.47 

O . 0068  ) 

O.OOO39  ) 

1 7-5 

19.2 

O.9I 

4400 

1 

0.096 

O . 0044 

50  sec. 
1200  “ 

r- 

6 6 

O . 0088  I 

O . OOO39  ) 

22.6 

21.9 

1.03 

to 


If  the  hypothesis  is  correct  — should  be  approximately  equal 

P* 

— . The  agreement,  though  unsatisfactory,  is  within  experi- 
p2 


mental  errors. 

It  is  here  assumed  that  light  of  a certain  intensity  acting  for 
twenty  minutes  will  produce  the  same  density  of  image  as  light  of 
twenty  times  the  intensity  acting  for  one  minute.  To  test  this, 
half  a plate  was  exposed  to  light  from  a point  source  at  a distance 
of  125  cm  for  45  seconds  and  the  other  half  was  exposed  for  720 
seconds  at  a distance  of  500  cm  from  the  same  source.  Here  the 
ratio  of  intensities  is  16  and  equal  to  the  inverse  ratio  of  the  times 
of  exposure.  No  difference  can  be  observed  between  the  densities 
of  the  two  halves  of  the  developed  plate — proving  that  for  the 
intensities  used  the  assumption  is  sufficiently  accurate. 

I gladly  acknowledge  my  indebtedness  to  Professor  C.  E. 
Mendenhall  for  help  in  designing  the  apparatus.  The  use  of  a 
capillary  in  combination  with  a Gaede  pump  to  secure  equilibrium 
conditions  and  thus  make  the  experiment  quantitative  was  sug- 
gested by  him. 

The  conclusion  from  this  experiment  is,  therefore,  that  the 
intensity  of  the  light  from  the  canal-ray  beam  is  proportional  to 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS  33 

the  pressure  of  the  gas  through  which  the  canal  rays  pass,  that  is, 
to  the  probable  number  of  collisions  per  unit  length  of  path,  per 
unit  time,  between  the  canal  rays  and  gas  molecules,  provided  that 
the  number  and  velocity  of  the  canal  rays  is  unchanged.1 

Next  the  question  arises,  how  does  the  intensity  of  the  light 
emitted  vary  with  the  velocity  of  the  rays  ? Does  it  vary  directly 
as  the  total  energy-flux  of  the  rays  times  the  gas  pressure,  that  is, 


Fig.  3. — Apparatus  for  measuring  the  energy-flux  of  the  canal  rays 


as  the  mean  energy  of  each  ray  times  the  number  of  collisions  per 
unit  length  of  path  per  second  ? To  answer  this  it  became  neces- 
sary to  measure  the  energy-flux  of  the  rays  as  a function  of  the 
cathode-fall  of  potential.  To  this  end,  they  were  allowed  to  strike 
inside  a light  silver  cone  so  that  their  kinetic  energy  might  be 
transformed  to  heat  energy  and  measured  from  the  temperature 
changes  produced. 

In  the  canal  chamber  the  apparatus  shown  in  Fig.  3 was  placed. 
The  silver  cone  weighing  only  a fifth  of  a gram  (3  cm  long  and  o . 5 
cm  in  diameter  at  its  base)  was  suspended  in  the  path  of  the  rays, 


1 This  result  was  reported  at  a meeting  of  the  Am.  Phys.  Soc.,  November  27,  1909. 


34 


GORDON  SCOTT  FULCHER 


by  means  of  silk  threads,  from  a grounded  aluminum  box  which 
served  to  shield  the  cone  from  sudden  changes  of  temperature. 
To  measure  the  instantaneous  temperature  of  the  cone  a thermo- 
couple was  used.  Along  one  side  of  the  cone  was  soldered  a con- 
stantan  wire  rolled  flat,  along  the  other  a copper  wire.  The  other 
junction  (see  Fig.  4)  was  maintained  at  a constant  adjustable 
temperature  by  immersion  in  kerosene  in  a Dewar  flask  provided 


Fig.  4. — Diagram  showing  the  electrical  connections  of  the  apparatus 


with  a heating  coil  and  stirrer.1  To  measure  the  thermo-electric 
current  a Thomson  galvanometer  was  used  whose  sensitiveness 
of  4X10-9  amperes  per  mm  deflection  could  be  decreased  by 
introducing  resistance  R2.  For  the  most  sensitive  adjustment 
used  (. R2  = o ),  1 mm  deflection  corresponded  to  about  o.ooi°C 
increase  in  temperature  of  the  cone  or  a net  addition  to  the  cone  of 
1 . 2X io-5  calories.  Two  telescopes  were  mounted  so  that  through 
one  the  observer  could  follow  the  second  hand  of  a watch  while 
noting  the  galvanometer  reading  with  the  other  eye.  Thus  a 
series  of  observations  at  intervals  of  5 seconds  could  be  made  and 

xTo  avoid  confusion,  the  discussion  of  other  details  of  the  apparatus  is  postponed 
to  the  end  of  the  paper. 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


35 


the  instantaneous  temperature  of  the  cone  as  a function  of  the 
time  determined.  Typical  curves  are  shown  in  Fig.  5.  On  start- 
ing the  discharge  through  the  tube  the  temperature  rises  rapidly 
at  first,  then  more  and  more  slowly.  The  curve  never  becomes 
horizontal  because  of  the  radiation  received  from  the  back  surface 
of  the  cathode,  which  increases  with  the  time  as  the  cathode  is 


o 1 Z 3 & S 6 7 6 MINUTES. 


Fig.  5. — Temperature  of  the  cone  as  a function  of  the  time 

heated  by  the  discharge.  At  the  instant  when  the  discharge  is 
stopped,  the  quickness  with  which  rapid  cooling  begins  is  note- 
worthy. Curves  XXI  and  XXX  were  taken  when  the  pressure 
in  the  canal  chamber  was  low  (0.005  mm),  while  curve  XXIV  was 
obtained  with  a much  higher  pressure  (0.1  mm).  The  sensitive- 
ness is  twice  as  great  for  XXIV  as  for  XXI  and  that  in  turn  twice 
as  great  as  for  XXX. 

The  problem  now  is  to  determine  the  value  of  the  energy-flux 


36 


GORDON  SCOTT  FULCHER 


corresponding  to  each  of  these  curves.  It  is  easily  shown  that  the 
temperature  is  in  no  case  a simple  exponential  function  of  the  time, 
as  would  be  the  case  if  the  heating  of  the  cone  by  the  rays  and 
the  radiation  of  heat  to  a constant  temperature  envelope  alone 
were  involved.  The  radiation  from  the  heated  cathode  is  an 
important  disturbing  factor.  If  we  let 
x=  temperature  of  the  cone, 
y = temperature  of  the  surrounding  gas  and  case, 
z = temperature  of  back  side  of  the  cathode, 
c=  heat  capacity  of  the  cone, 

E— energy  received  by  the  cone  from  the  canal  rays  per  second, 

A and  B = radiation  constants,  and 

C=  convection  constant  depending  on  the  gas  pressure, 

then 

c~  = E+A  (z-x)  — (B+C)(x-y)  (i) 

Just  preceding  the  instant  (£=5)  when  the  discharge  is  discon- 
tinued by  short-circuiting  the  tube  we  have 

C(^/)  =^'+^z5+(^+6')ys—  (A-\-B-\-C)xs  (2) 

while  immediately  following  the  cessation  of  the  discharge 

c(^di)+  ==^zs+(^+C')3;5—  (A+B-\-C)xs  (3) 

since  there  is  no  discontinuity  at  that  instant  of  either  x,  y,  or  z. 
Hence 


an  equation  which  serves  most  readily  for  the  determination  of 
E from  the  curves. 

(dx\ 

—J  accurately,  since  the 

cooling  was  so  rapid  at  first  that  the  galvanometer  readings  were 
uncertain  immediately  after  the  discharge  was  stopped.  The 
method  employed  was  a graphical  one.  A smooth  curve  was 
drawn  through  the  galvanometer  readings  plotted  as  a function 
of  the  time  (Fig.  5),  making  due  allowance  for  the  fact  that  the 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


37 


current  carried  by  the  rays,  which  in  part  passed  through  the  gal- 
vanometer, ceased  at  the  same  instant  as  the  discharge.  The 
ordinates  of  the  curve  were  read  at  regular  intervals  of  time  and 
the  values  of  the  time  derivatives  thus  obtained  were  plotted  as  a 


Time  derivative  of  the  temperature  of  the  cone  as  a function  of  the  time 


function  of  the  time.  Fig.  6 shows  two  such  derivative- time 
curves  corresponding  to  two  of  the  temperature-time  curves  of 
Fig.  5.  The  circles  were  obtained  from  the  cooling  part  of  the 
curves,  the  crosses  from  the  heating  part.  The  former  are  the  more 
reliable.  It  is  seen  that  a smooth  curve  can  be  drawn  through 
the  points  with  considerable  certainty  for  XXI  (low  pressure) 


38 


GORDON  SCOTT  FULCHER 


and  the  value  of  the  derivative  for  t = o can  be  determined  with 
some  accuracy.  A number  of  such  derivative-time  curves  are 
shown  plotted  to  the  same  scale  in  Fig.  7.  These  curves  were 
each  drawn  independently.  The  fact  that  they  fit  in  with  each 
other  so  well  is  evidence  for  their  accuracy. 

The  results  obtained  for  the  energy-flux  of  the  canal  rays  as  a 
function  of  the  cathode-fall  of  potential  are  plotted  in  Fig.  8.  It 


Fig.  8. — Energy-flux  of  canal-ray  bundle  as  a function  of  the  cathode-fall  of  potential 


is  to  be  regretted  that  the  agreement  between  the  various  points 
obtained  is  not  better.  The  trouble  does  not  lie  in  the  determina- 
tion of  the  energy-flux  from  the  curves,  since  that  is  probably 
accurate  to  a few  per  cent,  but  rather  in  the  measurement  of  the 
cathode-fall  of  potential.  The  Kelvin  electrostatic  voltmeter  could 
be  read  to  1 per  cent,  but  even  though  special  precautions  were 
taken,  as  will  be  described  later,  to  secure  a continuous  discharge 
through  the  tube,  the  cathode-fall  of  potential  was  seldom  quite 
constant,  so  that  readings  could  not  be  made  as  accurately  as 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


39 


otherwise.  The  effect  of  slight  impurities  in  the  gas,  such  as  were 
doubtless  given  out  by  the  cathode  during  the  discharge,  is  very 
marked,  though  in  no  cases  were  these  impurities  sufficient  to  affect 
the  spectrum  to  any  noticeable  extent.  It  is  seen  that  a change 
of  less  than  5 per  cent  in  the  abscissas  of  the  points  plotted  in  Fig. 
8 would  bring  all  of  them  on  the  curve  drawn  through  them.  We 


Fig.  9. — Ratio  of  light-intensity  to  gas  pressure  as  function  of  cathode-fall  of  potential 


must  conclude,  therefore,  that  the  curve  represents  the  experi- 
mental results  as  closely  as  possible  and  that  the  deviations  are 
less  than  possible  experimental  errors. 

The  variation  of  the  intensity  of  the  light  from  the  canal-ray 
beam  as  a function  of  the  cathode-fall  of  potential  was  determined 
precisely  as  in  the  first  experiment  by  photographing  the  beam, 
adjusting  the  times  of  exposure  so  as  to  obtain  images  of  about 
the  same  density.  The  results  are  plotted  in  Fig.  9.  The  ordinates 


40 


GORDON  SCOTT  FULCHER 


are  proportional  to  — , where  D is  the  density  of  the  image  meas- 
pt 

ured  with  a spectrophotometer,  p is  the  gas  pressure,  and  t the  time 
of  exposure.  Two  sets  of  determinations  were  made.  The  two 
curves  drawn  through  the  points  obtained  are  each  identical  with 
the  curve  shown  in  Fig.  8 except  for  a constant  factor  of  propor- 
tionality. The  ordinates  of  Fig.  8 are  proportional  to  the  mean 
energy  of  the  individual  rays  times  the  number  of  rays  striking 
the  cone  per  second  when  the  pressure  in  the  canal  chamber  is 
low;  that  is,  they  are  very  closely  proportional  to  the  mean  energy 
of  the  individual  rays  times  the  number  of  rays  emerging  from  the 
hole  in  the  cathode  per  second  when  the  pressure  is  the  same  on 
both  sides  of  the  cathode.  The  ordinates  of  the  curves  in  Fig.  g 
are  proportional  to  the  mean  intensity  of  the  light  emitted  as  a 
result  of  each  collision  times  the  number  of  rays  emerging  from 
the  hole  in  the  cathode  per  second  when  the  pressure  is  the  same 
on  both  sides  of  the  cathode.  The  fact  that  through  the  range  of 
cathode-falls  used  these  curves  agree  shows  that  the  mean  inten- 
sity of  light  emitted  per  collision  is  proportional  to  the  mean 
energy  of  the  individual  rays,  that  is,  to  the  mean  energy  of  each 
collision.  It  is  not  to  be  expected  that  this  law  holds  rigorously, 
and  deviations  may  be  expected  to  increase  as  the  minimum 
voltage  necessary  to  produce  a discharge  is  approached;  but 
within  the  limits  of  voltage  and  velocity  used  here  (1,500  to  5,000 

volts,  6 to  10X107  — ) the  law  seems  to  be  verified  within  the 
sec/ 

limits  of  experimental  error,  that  is,  within  a few  per  cent. 

DISCUSSION  AND  STATISTICAL  CALCULATIONS 

What  bearing  have  these  experimental  results  upon  the  theory 
of  the  production  of  the  light  in  question?  First,  it  must  be 
pointed  out  that  in  the  case  of  canal  rays  in  pure  hydrogen  the 
light  producing  the  displaced  lines  in  the  Stark  effect  is  several 
times  as  intense  as  that  producing  the  rest  lines,  hence  the  experi- 
mental results  which  apply  strictly  only  to  the  whole  of  the  light 
from  the  path  of  the  rays  may  be  taken  without  serious  error  to 
apply  to  the  light  from  the  moving  sources  alone.  The  experi- 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


4i 


ments  therefore  tend  to  prove  that  the  light  showing  the  Stark 
effect  is  emitted  only  as  a result  of  the  collisions  of  canal  rays  with 
gas  molecules  and  that  the  intensity  of  the  light  emitted  per 
collision  is  proportional  to  the  mean  energy  imparted  to  the  hit 
molecules  by  the  collisions. 

Can  the  details  of  the  Stark  effect  be  explained  on  this  basis  ? 
If  so,  what  additional  assumptions  are  necessary?  In  answering 
these  questions  a calculation  made  three  years  ago,  the  results  of 
which  were  reported  in  part  in  the  article  referred  to  above,  is  of 
some  importance.  By  a statistical  method  a computation  was 
made  of  the  Stark  effect  to  be  expected  if  the  following  assump- 
tions are  true: 

1 . That  canal  rays  all  with  the  same  velocity  enter  a gas  whose 
molecules  are  identical  with  the  rays  and  have  velocities  negligible 
in  comparison  with  that  of  the  rays; 

2.  That  the  momenta  after  collision  are  the  same  as  if  the 
colliding  molecules  were  perfectly  elastic  spheres; 

3.  That  the  intensity  of  the  light  emitted  by  each  hit  molecule 
is  proportional  to  the  kinetic  energy  given  it  as  a result  of  the 
collision,  but 

4.  That  no  light  is  emitted  by  a hit  molecule  unless  the  energy 
transmitted  to  it  exceeds  a certain  minimum,  which  is  supposed 
to  be  equal  to  the  energy  necessary  to  produce  ionization;  and 
finally 

5.  That  no  light  of  the  kind  in  question  is  emitted  by  the 
hitting  rays — the  supposition  being  that  they  are  for  the  most  part 
neutralized  by  the  collisions,  hence  do  not  emit  the  same  spectral 
lines  as  the  ionized  hit  molecules. 

Of  these  assumptions  the  first  two  are  made  for  the  sake  of 
simplicity.  Their  disagreement  with  the  actual  facts  in  the  case 
of  hydrogen  rays  in  hydrogen  gas  is  probably  not  sufficient  to 
affect  the  qualitative  value  of  the  computation.  The  third  assump- 
tion has  since  been  proved  by  the  experiment  described  above. 
The  last  two  are  equivalent  to  the>  single  assumption  that  the 
series-line  spectrum  is  emitted  only  by  the  molecules  which  become 
positively  charged  as  a result  of  the  shock  of  the  collision.  To  find 
out  whether  this  assumption  is  necessary  to  explain  the  details 


42 


GORDON  SCOTT  FULCHER 


of  the  Stark  effect,  as  reported  by  J.  Stark,  F.  Paschen,  and  B. 
Strasser,  on  the  basis  of  the  emission  of  light  only  as  a result  of 
molecular  collision  (necessitated  by  the  first  experiment  above), 
is  the  purpose  of  the  following  computations. 

The  method  employed  was  necessarily  statistical,  as  the  prob- 
lem is  too  complicated  to  yield  to  direct  mathematical  treatment. 
Using  the  second  assumption,  we  can  readily  determine  the  velocity 


Y 


of  the  hit  and  of  the  hitting  molecule  after  each  impact.  If  a 
molecule  with  velocity  u (Fig.  io)  hits  a molecule  at  rest  so  that 
the  line  of  centers  at  the  instant  of  collision  lies  in  the  XY  plane 
and  makes  an  angle  0 with  u,  the  resulting  velocities  are: 

(for  bit  molecule)  W'  = u sin  9 ; W'X=W'  (cos  0 cos  sin  9 sin  f) 
(for  hitting  molecule)  W =u  cos  9 ; Wx  — W (sin  9 cos  i/H-cos  9 sin  if) 

If  the  line  of  centers  is  not  in  the  XY  plane  but  its  projection 
on  a plane  perpendicular  to  the  velocity  of  the  hitting  molecule 
before  collision  ( W ) makes  an  angle  with  the  XY  plane,  and  if 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


43 


0'  is  the  angle  it  makes  with  W and  yfr'  is  the  angle  W makes  with 
the  X-axis,  then  after  the  collision, 

(for  hit  molecule)  V'  = W sin  0' ; 

V'x=  F'(cos  O'  cos  if/  — sin  O'  sin  </> ' cos  <f>) . 

(for  hitting  molecule)  V = W cos  O' ; 

Vx  = V (sin  6'  cos  ^'-f-cos  0'  sin  \f/'  cos  <f>) . 

Now  consider  Fig.  ii.  The  center  of  the  hitting  molecule 
at  the  instant  of  collision  must  lie  on  the  dotted  spherical  surface. 
Suppose  its  velocity  is  u.  It  can  readily  be  shown  that  if  the 


Fig.  13. — Various  groups  of  secondary  rays 


spherical  surface  is  divided  into  zones  by  coaxial  cones  whose 

angular  apertures  are  given  by  the  equations  cos2^=^,  where 

a is  an  integral  parameter  varying  from  1 to  10,  the  probability 
that  the  center  of  the  hitting  molecule  will  lie  within  any  one  zone 
is  the  same  since  the  areas  of  projection  of  the  zones  on  a plane 
perpendicular  to  u are  all  equal.  It  is  further  evident  that  if  each 
zone  is  divided  into  two  equally  probable  zones,  the  values  of  0 
corresponding  to  the  dividing  cones  will  be  equally  probable  values 
of  0.  If  then  we  assume  ten  collisions  for  a given  value  of  u 
such  that  the  line  of  centers  at  collision  makes  angles  with  u given 

by  the  equation  cos2  where  a has  values  0,1, 2,  . . . .8,9, 

the  resulting  velocities  after  collision  may  be  taken  to  represent 
fairly  the  actual  distribution  of  velocities  as  far  as  6 is  concerned. 


44 


GORDON  SCOTT  FULCHER 


These  equally  probable  rays  with  the  velocities  of  the  hit  and 
hitting  molecules  after  collision  in  each  case  are  shown  in  Fig.  n. 

The  general  method  of  treating  the  problem  in  hand  is  shown 
in  Fig.  12.  Canal  rays  are  assumed  to  enter  the  gas  all  moving 
with  the  same  velocity  u in  the  direction  of  the  X-axis,  which  is 
also  the  line  of  sight.  Let  each  ray  collide  with  a gas  molecule. 
The  distribution  of  velocities  among  this  first  generation  of  second- 
ary rays  (^4)  can  be  fairly  represented  for  our  purpose  by  the  ten 


bundles  of  rays  shown  in  the  XY  plane,  since  the  Doppler  effect 
depends  in  this  case  only  on  the  latitude  angle  0 and  not  on  the 
azimuth  angle  </>.  The  energy  given  the  hit  molecules  is  shown  in 
the  lower  half  of  the  same  diagram.  It  is  seen  that  by  far  the 
most  light  is  emitted  by  the  molecules  having  a considerable 
velocity  in  the  line  of  sight.  Let  us  assume  that  the  minimum 
energy  necessary  to  produce  ionization  is  some  fraction,  say  one- 
fifth  of  the  original  energy  of  each  canal  ray.  In  that  case  two  of 
our  bundles  of  hit  molecules  will  emit  no  light. 

Now  let  each  of  these  secondary  rays  strike  gas  molecules  and 
produce  another  generation  ( B ).  Here  the  Doppler  effect  will 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


45 


depend  on  both  and  6 ; hence  to  represent  this  generation  1,000 
bundles  of  hit  molecules  were  chosen,  ten  values  of  </>  (90  to  1710 
at  intervals  of  180)  for  each  value  of  6 and  ten  values  of  6 for  each 
value  of  the  angle  which  the  hitting  molecules  made  with  the 
X-axis  before  collision.  One  hundred  only  are  shown  in  perspec- 
tive in  the  drawing.  The  energy  and  the  x component  of  the 
velocity  of  each  of  these  bundles  was  computed  and  the  energy 
(taken  equal  to  the  square  of  the  velocity)  of  all  those  whose 


velocity  along  the  X-axis  lay  between  certain  limits,  say  0.50  to 
0.55  u , was  added  up  and  this  sum  was  taken  as  proportional  to 
the  intensity  of  light  corresponding  to  that  Doppler  shift.  Thus 
the  intensity  of  light  as  a function  of  the  Doppler  shift  to  be 
expected  from  this  generation  was  obtained  (BJ.  In  getting 
the  effect  of  the  third  generation  of  hit  molecules  a multiplication 
by  100  was  avoided  by  further  extending  the  principle  of  repre- 
sentation. The  cosine  of  the  angle  which  each  of  the  1,000 
rays  of  the  second  generation  made  with  the  X-axis,  was  computed 
by  dividing  the  velocity  of  each  ray  along  the  X-axis  by  its  actual 
velocity.  Then  these  values  of  the  cosine  were  plotted  as  a func- 
tion of  the  velocity,  one  point  for  each  ray.  These  were  divided 
into  groups  of  20  and  one  ray  picked  out  to  represent  each  20. 


46 


GORDON  SCOTT  FULCHER 


The  values  of  the  velocity  and  of  the  angles  yjr'  for  each  of  these 
50  representatives  were  obtained  directly  from  the  diagram. 
As  in  the  case  of  B,  ten  values  of  </>  for  each  of  ten  values  of  6 for 
each  ray  had  to  be  considered,  making  5,000  in  all,  for  each  of  which 
the  energy  and  velocity  along  the  X-axis  were  computed.  The 
intensity  of  light  as  a function  of  the  Doppler  shift  was  then 
obtained  as  before  (Cz). 

We  have  considered  so  far  only  the  secondary  rays  in  one  direct 


Fig.  17. — Stark  effect  for  hydrogen 


line  of  descent,  both  in  the  emission  of  light  and  in  the  production 
of  other  secondary  rays.  But  surviving  each  generation  of  collisions 
there  are  in  addition  to  the  ionized  hit  rays  some  positively  charged 
hitting  rays  which  failed  to  ionize  the  molecules  they  hit  but  were 
merely  deflected.  In  the  diagram  (Fig.  13),  the  full  lines  represent 
hit  ionized  molecules  which  emit  light;  the  dashed  lines  represent 
ionized  hitting  molecules,  emitting  no  light  but  capable  of  pro- 
ducing other  ionized  secondary  rays  which  may  emit  light.  In 
Fig.  21  the  Doppler  effect  due  to  each  of  these  groups  of  rays, 
on  the  basis  of  the  assumptions  made  at  the  beginning,  is  shown 
(Ax,  Bx,  B2,  CXj  C2,  C5,  Cft)  for  the  special  case  when  the  energy  of 
each  canal  ray  is  taken  to  be  five  times  the  minimum  energy 
necessary  to  produce  ionization  (R=  5).  The  total  Doppler  effect 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


47 


for  each  generation  for  the  same  case  is  shown  in  Fig.  14.  The 
distribution  of  the  light  due  to  the  later  generations  was  obtained 
by  extrapolation,  using  the  curves  shown  in  Fig.  15.  The  sum 
of  them  all  shows  discontinuities  at  o . 2 u and  u due  to  our  artifi- 
cial assumption  that  all  the  canal  rays  have  the  same  velocity 
and  that  the  unshifted  line  has  no  width.  By  modifying  these 
assumptions  to  agree  more  closely  with  the  actual  facts  the  dis- 
continuities are  eliminated.  The  results  for  the  cases  when  R=  2 


and  R=S  are  given  in  Fig.  16.  It  was  assumed  in  getting  the 
scale  of  abscissas  that  the  minimum  energy  necessary  to  produce 
ionization  corresponds  to  a velocity  of  2X107  cm  per  sec.  in  the 
case  of  hydrogen.  For  comparison  with  the  Stark  effect  as  actually 
observed,  an  intensity-velocity  curve  has  been  reprinted  from 
Professor  F.  Paschen’s  paper1  (Fig.  17).  This  curve  is  obviously 
the  sum  of  two,  each  having  a marked  intensity  minimum  and 
agreeing  in  general  form  with  the  two  computed  curves  shown  in 
Fig.  16.  A better  agreement  could  hardly  be  expected. 

To  show  the  necessity  of  introducing  the  fourth  assumption 
regarding  the  minimum  energy  necessary  to  produce  ionization, 

1 Annalen  der  Physik,  23,  250,  1907. 


48 


GORDON  SCOTT  FULCHER 


a calculation  was  made  without  this  assumption.  The  result  for 
the  case  when  R=  2 is  shown  in  Fig.  18  (a).  Curve  ( b ) is  repro- 
duced from  Fig.  16  for  comparison.  Evidently  the  presence  of 
the  intensity  minimum  demands  this  fourth  assumption. 

The  fifth  assumption,  that  no  hitting  rays  emit  light  as  a result 
of  the  collisions,  seems  rather  arbitrary  and  it  appeared  desirable 

to  determine  to  what  extent  this 


• - nrr  molecules  emoting  light 
© - ffrrriMs  hays  emitting  light 
© - CHARGED  nays  not  emitting  light 


assumption  is  necessary.  If  we 
assume  that  each  of  the  charged 


O - NEUTRAL  HAYS. 
( ) - SLOW  HASS 


lOOOM/5-9— 


300- 


-200-9— 


216-%  C, 
156  -© 

60  -O 
‘-YJSW-O 
124--%  C, 
92-9 
32.-0 
W-esaK) 

46-%  Q 
14 

2400-^321 

124-0 
'-(6400  '-1264)0 
f-ISOJ-O  1 - S3 -%  C, 
M-  53-9 
400 
Ul340 
29-%  C, 


-160- 


r- 


M4 OOhO 


'-6OOO— 


22- O 

r 32  ~%  Cr 

1200 — ^ 
f-  840 
'-(92)0 
1-14600  r 76-%  C, 
-/60-f^h  64-9 
60-$Y  12  O 
*-(288)0 

-000)0  r-  85-%  C„ 

f-  26- 

4200— \-f591 
Y-2290 
W44DO 


& 


Fig.  20. — Genealogy  on  the  basis 
of  the  six  assumptions 


hitting  molecules  emits  light  whose 
intensity  is  proportional  to  the 
energy  of  the  collision,  a calcula- 
tion of  the  Doppler  effect  due  to 
this  light  gives  curves  shown  in 
Fig.  19.  Here  again  the  presence 
of  the  intensity-minimum  in  the 
Stark  effect  proves-  that,  for  the 
most  part  at  least,  the  charged 
hitting  rays  do  not  emit  any  light 
corresponding  to  the  series-line 
spectrum  as  a result  of  the  col- 
lisions. 

There  is  still  a further  possi- 
bility to  be  investigated.  Neutral 
rays  when  moving  with  sufficient 
velocity  doubtless  have  the  power 
of  producing  ionization.  If  so, 
the  hitting  molecule  is  as  likely 
to  be  ionized  as  the  hit  molecule. 
Nothing  is  known  as  to  the  mini- 


mum energy  necessary  to  produce  ionization  in  this  case,  but 
a calculation  was  made  adding  the  following  assumption  to  the 


five  considered  above: 

6.  That  when  the  collision  of  a'neutral  ray  with  a neutral  gas 
molecule  involves  the  transference  of  more  than  a certain  mini- 


mum energy,  which  is  assumed  to  be  equal  to  the  minimum  energy 
necessary  for  ionization  in  the  case  of  the  collision  of  a charged 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


49 


ray  with  a gas  molecule,  one  will  be  ionized  so  that  on  the  average 
half  the  hitting  and  half  the  hit  molecules  will  emit  light. 


cz 


Fig.  2i. — Doppler  effect  due  to  various  groups  of  secondary  rays 


The  introduction  of  this  assumption  adds  several  groups  of 
active  rays  to  our  family.  The  genealogy  for  the  case  of  1,000 
positively  charged  rays  (R=  5)  is  given  in  Fig.  20.  The  slow  rays 


5o 


GORDON  SCOTT  FULCHER 


are  those  incapable  of  producing  ionization.  The  Doppler  effect 
corresponding  to  each  of  the  active  groups  of  rays  was  computed 
for  the  first  three  generations.  The  curves  are  shown  in  Fig.  21. 
The  effect  of  later  generations  was  obtained  by  extrapolation  as 
above  (cf.  Fig.  15).  The  total  effect  due  to  1,000  charged  canal 
rays  on  the  basis  of  the  six  assumptions  is  shown  in  Fig.  22  ( a ) 
for  the  special  case  when  R—  5.  Curve  ( b ) is  reproduced  from 
Fig.  16  for  comparison.  Evidently  our  sixth  assumption  is  incom- 


tion 

patible  with  an  intensity  minimum.  Probably  the  minimum 
energy  required  for  neutral  rays  to  produce  ionization  is  much 
greater  than  was  assumed  and  hence  the  disturbing  effect  of  these 
neutral  rays  is  much  less.  Finally  a computation  was  made  of 
the  Doppler  effect  to  be  expected  on  the  basis  of  the  six  assump- 
tions if  1,000  neutral  canal  rays  with  the  same  velocity  u enter  a 
gas.  The  genealogy  in  this  case  is  similar  to  that  shown  in  Fig. 
20  except  that  the  number  in  the  various  groups  is  quite  different. 
The  total  Doppler  effect  due  to  these  1,000  neutral  rays  and  their 
offspring  is  shown  in  Fig.  23  for  the  special  cases  when  R=  2 and 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


51 


R=  5.  Here  again  it  is  evident  that  the  number  of  neutral  rays 
must  be  small  or  assumption  6 must  be  incorrect.  The  number 
of  neutral  rays,  however,  is  known  from  deflection  experiments 
not  to  be  small,  may  be  in  fact  over  30  per  cent  of  the  whole  number. 
The  other  alternative  is  therefore  inevitable. 

' CONCLUSIONS  ' 

As  a result  of  these  calculations  one  seems  justified  in  concluding 
that  the  original  assumptions  regarding  the  minimum  energy 
necessary  to  produce  the  emission  of  light  and  the  emission  of  light 
by  the  hit  ionized  molecules  alone,  represent  the  true  state  of  the 
case  very  approximately.  If  the  neutral  rays  produce  ionization, 
the  minimum  energy  required  must  be  considerably  greater  than 
is  necessary  in  the  case  of  charged  rays,  so  that  the  light  thus  pro- 
duced is  insignificant.  The  hitting  charged  rays  must  be  neutral- 
ized for  the  most  part  and  particularly  when  the  shock  of  collision 
is  great,  at  the  same  instant  as  the  hit  molecule  is  ionized. 

If  this  analysis  of  the  phenomenon  is  correct,  a far  more  impor- 
tant conclusion  necessarily  follows:  namely,  that  the  series-line 
spectrum  of  hydrogen,  which  alone  shows  the  Stark  effect,  is 
emitted  by  the  positively  charged  molecule  or  atom  of  hydrogen. 
The  reasoning  leading  to  this  deduction  may  seem  rather  indirect, 
but  the  fact  that  the  above  assumptions  are  the  only  ones,  as  I 
believe,  which  will  explain  the  presence  of  the  intensity  minimum 
in  the  Stark  effect  on  the  basis  of  the  experimentally  verified 
hypothesis  that  the  emission  of  light  in  the  path  of  the  canal  rays 
is  due  to  the  collision  of  the  canal  rays  and  their  offspring  with 
gas  molecules,  is  strong  evidence  for  their  correctness.  Some 
other  experiments  will  be  performed  shortly  to  test  some  further 
deductions  from  this  analysis  of  the  phenomenon. 

DISCUSSION  OF  STRASSER’S  RESULTS 

Last  April  in  the  Annalen  der  Physik ,x  B.  Strasser  published 
some  results  of  his  painstaking  experiments  on  the  Stark  effect 
which  are  of  great  interest.  May  I make  a few  suggestions  as  to 
a possible  interpretation  of  these  results  along  the  same  line  as 
1 Annalen  der  Physik,  31,  890-918,  1910. 


52 


GORDON  SCOTT  FULCHER 


in  the  case  of  the  simple  Stark  effect  in  pure  hydrogen?  Here 
again  one  is  working  rather  in  the  dark,  but  a suggestion  may 
have  value  as  a working  hypothesis  even  though  it  later  proves 
to  be  false. 

Strasser  has  proved  the  following  facts: 

1.  The  intensity  of  the  rest  line  in  the  Stark  effect  for  hydro- 
gen canal  rays  depends  on  the  purity  of  the  hydrogen  in  the  tube. 
If  the  gas  is  sufficiently  pure  no  rest  line  is  obtained. 

2.  If  a definite  quantity  of  another  gas  is  added,  the  intensity 
of  the  rest  line  is  increased  and  that  of  the  shifted  line  decreased  in 
proportion  to  the  amount  added,  so  that  when  a sufficient  quan- 
tity of  the  foreign  gas  is  present  an  intensity  minimum  is  no  longer 
obtained  between  the  two  lines. 

3.  By  experimenting  with  various  gases  (N,  Ar , He)  it  was 
found  that  the  effect  produced  when  the  partial  pressure  of  the 
added  gas  had  a certain  value  was  greater  the  larger  the  atomic 
weight  of  the  gas  introduced. 

From  these  results  it  seems  evident  that  the  rest  line  is  due  to 
the  collision  of  hydrogen  canal  rays  with  molecules  of  the  foreign 
gas.  The  larger  the  number  of  molecules  of  the  foreign  gas  present, 
the  greater  the  number  of  collisions  with  them  in  proportion  to  the 
number  of  collisions  with  hydrogen  molecules  which  we  have 
assumed  produce  the  displaced  line.  If  we  assume  that  the 
charged  canal  rays  are  not  neutralized  for  the  most  part  by  col- 
liding with  foreign  gas  molecules,  but,  because  of  the  shock  of  the 
collision,  emit  light  whose  intensity  is  proportional  to  the  energy 
of  the  collision,  the  Doppler  effect  due  to  this  light  would  resemble 
in  general  form  the  curves  shown  in  Fig.  19,  though  modified  by 
the  fact  that  in  this  case  the  hit  molecules  are  larger.  Thus  we 
should  expect  the  rest  fine  to  be  broadened  unsymmetrically  toward 
the  displaced  line  as  Strasser  found.  Moreover  gases  with  greater 
atomic  weights  may  be  expected  to  have  larger  molecules,  hence' 
to  exert  a greater  influence  for  a given  number  of  molecules  by 
increasing  the  probability  of  being  struck  by  the  canal  rays.  The 
only  difficulty  is  to  explain  why  the  hydrogen  canal  rays  are  neu- 
tralized for  the  most  part  when  striking  hydrogen  molecules  but 
not  when  hitting  other  molecules.  But  Strasser  has  shown  that 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


53 


the  Doppler  effect  produced  in  the  two  cases  is  quite  different. 
It  is  hard  to  see  how  the  facts  can  be  explained  otherwise. 

Strasser  also  reports  that  the  light  from  the  layer  just  in  front 
of  the  cathode  shows  a weak  displaced  line  with  a distinct  intensity 
minimum,  whereas  immediately  behind  the  cathode  a strong, 
broad  displaced  line  is  obtained  corresponding  to  the  high  velocity 
of  the  canal  rays.  The  explanation  seems  to  be  that  as  the  canal 
rays  acquire  their  velocity  through  the  action  of  the  electric  field 
in  front  of  the  cathode,  and  since  the  potential-gradient  is  extremely 
steep  right  near  the  cathode,  the  number  of  rays  having  a velocity 
high  enough  to  produce  ionization  must  increase  very  rapidly  just 
at  the  surface  of  the  cathode.  This  leads  to  the  apparent  discon- 
tinuity at  the  surface  of  the  cathode  which  suggested  Strasser  and 
Wien’s  theory  that  the  canal  rays  emit  light  as  a result  of  the 
electric  shock  experienced  in  suddenly  passing  from  a very  strong 
to  a weak  field — a hypothesis  which  of  course  is  no  longer  tenable. 

Strasser’ s observation  that  the  hydrogen  lines  persist  to  a 
greater  distance  from  the  cathode  than  the  lines  of  a foreign  gas 
may  be  interpreted  to  show  that  the  minimum  energy  required  to 
produce  the  emission  of  light  is  greater  in  the  case  of  the  foreign 
gas  than  in  the  case  of  hydrogen.  Finally  Strasser  reports  that 
the  spectrum  of  the  light  from  the  path  of  the  canal  rays  viewed 
normal  to  their  velocity  shows  the  same  broadening  of  the  lines 
whether  there  is  a foreign  gas  present  or  not.  The  computation 
of  the  effect  to  be  expected  on  the  basis  of  the  five  assumptions 
made  above  is  extremely  laborious,  but  a first  approximation 
shows  a fair  qualitative  agreement  with  this  experimental  result. 
Strasser  does  not  publish  quantitative  data  as  to  the  amount  of  the 
broadening.  His  more  recent  results  for  hydrogen  canal  rays  in 
nitrogen  gas1  can  obviously  be  explained  in  the  same  way  as  these 
earlier  ones  and  merely  add  to  the  evidence  in  support  of  this 
analysis  of  the  phenomenon. 

CONDUCTION  OF  HEAT  BY  A GAS  AT  LOW  PRESSURE 

The  curves  shown  in  Figs.  5 and  6 give  some  idea  of  the  relative 
importance  of  convection  and  of  radiation  in  the  cooling  of  the 
1 Annalen  der  Physik,  32,  1107,  1910. 


54 


GORDON  SCOTT  FULCHER 


cone.  Curve  XIV  was  made  with  the  pressure  in  the  canal  cham- 
ber about  twenty  times  as  great  as  when  curve  XXI  was  taken. 
From  the  derivative  curves  (Fig.  6)  it  appears  that  the  energy 
being  received  by  the  cone  per  second  in  the  first  case  is  even 
greater  than  in  the  second  case  yet  the  maximum  temperature 
reached  in  the  first  case  is  only  one-sixth  of  that  reached  in  the 
second  case.  By  differentiating  equation  (3)  we  get 

since  the  time  derivatives  of  z and  y are  negligible  in  comparison 

doc 

with  ~ for  the  cooling  part  of  the  curve.  This  enables  a rough 

Cl  l 

determination  of  to  be  made.  The  results  show  a 

surprisingly  good  agreement.  The  value  increases  from  0.00010 
calories  per  second  at  a pressure  of  0.005  mm  to  -00065  calories 
per  second  at  a pressure  of  o . 1 mm  of  mercury — showing  that  at 
the  higher  pressure  convection  is  at  least  ten  and  probably  twenty 
times  as  important  as  radiation  in  cooling  the  cone.  The  conduc- 
tion coefficients  computed  from  these  data  are  about  0.00017  and 
0.000013  calories  per  second  per  degree  C.  per  cm3  for  pressures  of 
0.1  mm  and  0.005  mm  respectively.  By  comparison  with  the 
coefficient  for  hydrogen  at  ordinary  pressures,  which  is  given  by 
Meyer  as  0.00040,  it  is  seen  that  the  coefficient  must  be  nearly 
constant  until  pressures  below  1 mm  of  mercury  are  reached. 

PROPORTION  OF  NEUTRAL  CANAL  RAYS 
From  the  energy-flux  of  the  canal  rays  it  is  possible  to  compute 
the  lower  limit  to  the  number  striking  the  cone  per  second  by 
dividing  the  energy-flux  by  the  energy  a singly  charged  molecule 
would  have  if  acted  on  by  the  whole  cathode-fall  of  potential. 
Curve  I of  Fig.  24  was  thus  computed  from  the  curve  in  Fig.  8. 
A lower  limit  to  the  number  charged  could  be  obtained  by  dividing 
the  current  carried  by  the  rays  to  the  cone  by  the  known  value 
of  e.  Thus  curve  II  was  computed.  The  increase  in  the  propor- 
tion of  neutral  rays  with  the  increase  in  the  cathode-fall  of  poten- 
tial is  to  be  expected,  I think,  for  the  particular  form  of  tube  which 
was  used,  though  it  might  not  be  true  for  another  tube. 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS 


55 


description  oe  apparatus  ( Continued ) 

To  admit  the  gas  at  a uniform  rate  a capillary  was  used.  The 
best  dimensions  were  determined  by  the  use  of  Knudsen’s  formula.1 


2000  2JOO  3000  3500  4000  45(00  WITS. 


Fig.  24 


A number  of  capillaries  were  drawn  and  left  attached  to  tubes  of 
larger  bore.  The  method  employed  to  measure  them  is  illustrated 
in  Fig.  25.  Mercury  was  forced  part  way  into  the  capillary  from 
the  larger  tube  by  means  of  a rubber  bulb,  and  the  capillary  was 


Fig.  25. — Calibration  of  a capillary  tube 


calibrated  by  noting  the  corresponding  distances  moved  by  the 
two  ends  of  the  mercury  thread.  From  the  diameter  of  the  larger 
tube  that  of  the  smaller  could  thus  be  readily  calculated. 

To  remove  the  mercury  vapor  from  the  gas,  it  was  passed  first 


1 Annalen  der  Physik,  28,  75,  1909. 


56 


GORDON  SCOTT  FULCHER 


through  flowers  of  sulphur  and  copper  filings  to  remove  the  sulphur 
vapor,  then  through  a coil  kept  immersed  in  a freezing  mixture  of 
solid  C02  and  ether.  All  traces  of  the  mercury  lines  disappeared 
from  the  discharge  tube  with  this  arrangement. 

To  secure  a continuous  discharge  the  following  arrangement 
was  hit  upon  (see  Fig.  4).  An  induction  coil  was  used  to  keep  a 
capacity  charged  by  periodically  sparking  across  a point-and- 
plane  gap  made  sufficiently  long  to  prevent  back  sparking.  This 
capacity  of  0.3  microfarad  was  allowed  to  discharge  slowly  and 
continuously  through  a resistance  of  several  hundred  thousand 
ohms  (made  by  rubbing  graphite  on  a plate  of  ground  glass)  which 
was  placed  in  series  with  the  discharge  tube.  No  discontinuities 
in  the  discharge  could  be  observed  with  a rotating  mirror.  After 
the  induction  coil  was  stopped  the  luminous  discharge  would 
continue  sometimes  for  over  a minute.  The  discharge  therefore 
was  probably  quite  continuous.  If  the  induction  coil  was  connected 
to  the  tube  directly,  producing  a discontinuous  discharge,  a spark- 
gap  of  one  centimeter  would  short-circuit  the  tube  if  placed  in 
parallel  with  it,  whereas  if  the  condenser  set-up  was  used  with  the 
same  pressure  in  the  tube,  5,000  volts  would  maintain  a contin- 
uous discharge  through  the  tube.  Other  evidence  was  secured 
tending  to  show  that  a continuous  discharge  is  an  unstable  phe- 
nomenon unless  very  special  precautions  are  taken;  and  that  the 
mean  discharge  potential  is  always  greater  in  the  case  of  the  dis- 
continuous discharge  than  in  the  case  of  the  continuous,  though 
much  less  than  the  maximum  value  reached  by  the  oscillating 
potential-difference  in  the  former  case.  A rotating  mirror  should 
always  be  used  to  test  the  continuity  of  the  discharge  in  the  case 
fo  any  quantitative  experiments  involving  the  discharge  of  electricity 
through  gases. 

My  thanks  are  due  to  Professor  A.  G.  Webster  for  his  interest 
and  encouragement  during  my  stay  at  Clark  University,  where  the 
above  theory  was  developed. 

Madison,  Wis. 

December  28,  1910 


THE  PRODUCTION  OF  LIGHT  BY  CANAL  RAYS  57 
ADDENDUM 

By  a strange  mischance  I failed  to  see,  until  the  above  was  in 
type,  an  article  by  Professor  W.  Wien1  in  which  he  gives  results  of 
his  measurements  of  the  luminosity  of  a canal-ray  beam  at  various 
pressures.  He  finds  that  the  luminosity  increases  with  the  pres- 
sure, in  qualitative  agreement  with  my  observations,  but  a quan- 
titative comparison  would  be  difficult  because  of  the  complexity 
of  the  conditions  existing  with  his  form  of  apparatus.  His  inter- 
pretation of  the  results  is  quite  different  from  mine. 

1 Annalen  der  Physik,  30,  349-368,  1909. 


